Gyroscopic directional reference systems for piloting and automatic flight control usually consist of a gyroscope having two degrees of freedom and a pendulous two-gimbal suspension, or alternatively a set of three single degree of freedom gyros, either on a gimballed platform or strapped down to the air frame. While throughout this specification and claims the term "aircraft" is used to describe the vehicle in which the heading reference system is located, it should be understood that the invention is equally as well applicable to any type of vehicle which changes its heading direction by rolling or banking of its lifting surfaces, for example hydrofoil vehicles, and the term "aircraft" is meant to include such. A single gyroscope having two degrees of freedom is mechanically complicated and is subject to tumbling problems during maneuvers. In contrast, a three-gyroscope arrangement of single degree of freedom gyros is electrically complicated and relatively expensive. Improved reliability through redundancy for the three-gyroscope arrangement using single degree of freedom gyros typically requires three additional gyros, or six gyros altogether, at significant increase in cost and complexity. Typically with such three-gyro arrangements of single degree of freedom gyros, there is required in addition two accelerometers for alignment.